The following data were collected in an experiment to study the relationship between extrusion pressure (in KPa) and wear (in mg). x 150 175 200 225 250 275 y 10.4 12.4 14.9 15 13.9 11.9 The least-squares quadratic model is y=-32.44571429 +0.43154286x-0.00098286x² + Using the given equation, compute the residuals. (Round the final answer to five decimal places and include a minus sign if necess y 150 10.4 175 12.4 200 14.9 225 15 250 13.9 275 11.9 Residual
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- The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02Consider the model Ci= B0+B1 Yi+ ui. Suppose you run this regression using OLS and get the following results: b0=-3.13437; SE(b0)=0.959254; b1=1.46693; SE(b1)=0.0697828; R-squared=0.130357; and SER=8.769363. Note that b0 and b1 the OLS estimate of b0 and b1, respectively. The total number of observations is 2950. The number of degrees of freedom for this regression is A. 2950 OB. 2948 OC. 2952 OD. 2A representative sample of 190 students resulted in a regression equation between y = left hand spans (cm) and x = right hand spans (cm). The least squares regression equation is y = 1.4 + 0.97 x. For a student with a right and left hand span of 24 cm, what is the value of the residual? Give your answer to 2 decimal places.
- A study was conducted to assess the relationship between students’s score in final exam (y) and number of hours spent for exam (x) in each day. Data on a random sample 20 students were obtained and a regression model was estimated; and the least squares estimates obtained are: intercept a=28.5 and slope b=4.3 with SE(b)=Sb=0.017. The SS are: TSS=2540 and ESS=850. ****** QA) What is the difference between exam score obtained by two students one who studied 5 hours and the other who studied 9 hours per day. QB) In the above Question 1, find 95% CI for the slope and interpret it. In the above Question 1, find and interpret the coefficient of determination (r-square value).The prelim grades (x) and midterm grades (y) of a sample of 10 MMW students is modeled by the regression line y = 12.0623 + 0.7771x. Estimate the prelim grade if the midterm grade is 83.The peanut crop was harvested from five fields of various area. The following data are the mass of the crop from each field y (in kilograms) and the field area x (in hectares). X 6² Round your intermediate answers to four decimal places (e.g. 98.7654). (a) Fit the simple linear regression model using the method of least squares. Find the estimate of ². Round your answer to the nearest integer (e.g. 9876). i B₁ = (b) What change in the mean mass is expected when the field area changes by 1 hectare? Round your answer to the nearest integer (e.g. 9876). ŷ: 7280 15730 13590 19820 12860 = 2.01 3.93 3.68 4.33 2.33 (c) Calculate the fitted value of y corresponding to x = 2.01. Find the corresponding residual. Round your answer to the nearest integer (e.g. 9876). =
- A least squares regression line was calculated to relate the length (cm) of newborn boys to their weight in kg. The line is weight = -5.66 +0.193 length. A newborn was 48 cm long and weighed 3 kg. According to the regression model, what was his residual? What does that say about him? What was his residual? kg (Round to three decimal places as needed.)Using 81 quarterly observations on the growth rate of employment (Y) and the growth rate of output (X), the following regression results are obtained by ordinary least squares (t = 1, 2,...,81): -0.002+0.105X+0.730Y-1+0.063X-1, (0.001) (0.014) (0.045) (0.016) BG 1.100 [0.363], WH=1.474 [0.175], RESET = 0.081 [0.777], R² = 0.8827, SSR 0.00061, -0.002+0.086(X+X-1)+0.711Y-1, (0.001) (0.011) (0.045) R² = 0.8767, SSR = 0.00065. is the fitted value of the regression; figures in parentheses are the standard errors of the estimated coefficients; R² is the coefficient of determination; SSR is the sum of squared residuals; BG is the Breusch-Godfrey test for fourth-order autocorre- lation; WH is White's test for heteroskedasticity; RESET is Ramsey's regression specification error test; figures in square brackets are the p-values of BG, WH and RESET. Test the null hypothesis that the coefficients on X and X-1 in the first regres- sion are equal against the alternative hypothesis that they are not…The estimated least-squares regression equation for profit (in $100,000) is: y' = 2.5 + 0.054t Sales for time period 32 (t = 32) are 5% below the average of yearly sales. Forecast sales, including the seasonal component, for t = 32.
- The data in the accompanying table include the appraised value, land area of the property in acres, and age, in years, for a small sample of 30 single-family homes in a small city. Perform a multiple regression analysis to predict appraised value based on land area of the property X1 and age, in years, X2 and determine the VIF for each independent variable in the model. Is there reason to suspect the existence of collinearity? Determine the VIF for each independent variable in the model.Fit a curve of the form g(x) = A10Bx to the dataset using the Least Squares Method. Calculate the corrected values and the total squared error.A study was conducted among a smaple of undergraduate students to find the relationship between the number of cups of coffee consumed (x) and level of anxiety (y). The following least squares regression equation was obtained as a result of the study: ý = 0.3 + 0.0342z The obtained regression equation implies which of the following? Each cup of coffee consumed increases anxiety level by 30.0% Each cup of coffee consumed increases anxiety level by an average amoint of 3.42% Each cup of coffee consumed increases anxiety level by exactly 3.42% Anxiety level increases by 1 unit as a result of consuming 0.3 cups of coffee